psychrometry: from partial pressures to mole …

NIJOTECH VOL. 4 NO. 1 MARCH 1980 EZEILO 43

PSYCHROMETRY: FROM PARTIAL PRESSURES TO MOLE FRACTIONS

by

Clifford C.O. Ezeilo

Department of Mechanical Engineering

University of Nigeria, Nsukka.

(Original Manuscript received, January 15, 1980.)

ABSTRACT

This study uses the viria1 and interaction coefficients of the normal air

components in deriving compressibility factors and thereafter a simple

iterative formulation for mole fractions. Conversion from partial

pressures to mole fractions now becomes tractable by means of determinate

multipliers. The results obtained compare most favourab1y with the widely

accepted derivations due to Goff and Gratch. One possible advantage is

that the presented formulation permits the evaluation of those

multipliers without reference to the virial and interaction coefficients

provided that the "dry air" and moist air compressibility’s are very

accurately measured. A possible simplification is that this partial

pressure multiplier is expressed explicitly in a form suggesting

acceptable results for air-water gaseous mixtures outside the range of

normal air psychometry.

NOTATION

P pressure (m-bar)

V specific volume (m3/Kg-mole)

RO universal gas constant =

0.083143

m3 bar/Kg-mole. K

= 8.3143 KJ/Kg-mole. K

T absolute temperature (K)

Z compressibility factor

(dimensionless)

B, B’,A11, Aaa, Aww = second virial

Coefficients

(consistent units)

C,C’ A111’ A aa a, Awww = third virial

Coefficients

(consistent units)

D Fourth virial coefficient

(consistent units)

X Mole fraction (dimensionless )

K Boltzmann constant =1.39053

X10-23 (j/k)

N Avogadro number = 6.023 x

1026/KG- mole

Ε Maximum negative value of the

molecular potential energy (J)

Q Closest approach o two

molecules considered as rigid

spheres (m)

Angstrom unit = 1.0x10-10 meter

T* reduced temperature:. T(k/ɛ).

(dimensionless)

B* reduced second virial

coefficient

= B/ . (dimensionless)

bo second viral from the potent

malfunction= 2 No3/3 (m3/Kg-

mole)

f pressure multiplier

(dimensionless)

w specific humidity (g/kg dry

air)

Subscripts

ss state of air saturated with

water vapour

a dry air alone

w water vapour alone

aa molecules of air in pairs also

air alone in mixture

ww water molecules in pairs also

water alone in mixture

aw air and water molecules also

air watersecond virial

interaction in the binary

mixture

aaa air molecules in threes also

the third virial coefficient

for air alone

vww water molecules taken in

threes also water alone in the

third viral coefficient

aww,aaww air-water third virial

interactions: one air plus two


water molecules and one water

plus two molecule of air

1. INTRODUCTION

The earliest studies of

psychrometry considered normal air

as an ideal gas mixture. Partial

pressures then become identical:

to mole fractions and sets of

psychometric parameters result

from rather elementary

thermodynamic relations. Search

for more accurate data has long

led to the realization that

neither dry air nor pure water

vapour behaves like an ideal gas,

despite the fact that the dry air

component normally exists at

temperatures far inexcess of the

critical point temperature while

the vapour pressure is much below

the critical pressure of steam.

This destroys the Gibbs-Dalton law

as a basis for standardization.

Modifications of the

classical ideal gas equation of

state to fit the observed data

have been made by many

investigators. Most of these

efforts take the form of measuring

the compressibility factors of dry

air, water vapour and their binary

mixtures at various mixing ratios

and thereafter expressing the P-V-

T data as a virial equation of

state. Thus from the simple

relation

PV = RO T (ideal gas) (1)

we have the equations

PV/ROT=Z=1+B/V+C/V2+D/V

3+(Volume

series) (2)

and

PV/ROT = Z = 1+ B1 P +C

1P2 + ……..

(Pressure series) (3)

The above two expressions are

virial equations of state in which

the second and third virial

coefficients are related in the

form

B1 = B/(ROT) and C

1= (C-B

2) /(ROT)

2

(4)

Writing

PV/ROT = 1- 211111 P

TR

A

TR

A

OO

(5)

it would follow that

A11 = -B (6)

and A111 = -(C –B 2) /(ROT) (7)

A11 the virial coefficients: B, C,

B 1, C1, A11 and A111 are

functions of temperature and some

often tabulated for single

component gases.

For air as a single component gas

Zaa = PV/ROT = 1 – (P/ROT)Aaa

- aaa

O

ATR

P

2

(8)

Similarly for water vapour,

Zww = (PV/ROT) = 1 – (P/ROT)Aww -

(p2/ ROT)Aww (9)

When two or more dissimilar gases

form a mixture, interaction force

constants complicate the analysis.

In the case of binary mixture of

dry air and water vapour

Zaw = PV/RTO = 1 - P/RoT[ Aaa+ 2xa

xwAaw + Aww] (11)

where Aaw is the interaction

coefficient between the air and

vapour molecules considered in

pairs. In eqn.10 the series is

restricted to the second virial

and interaction coefficients only.

This restriction has been

identified as the "Three Liquid

Theory" of binary gas mixtures in

statistical thermodynamics.

If the third viral and

interaction coefficients are also

known, then, considering the

molecules in groups of threes will

extend eqn.10 into the longer

series relation

Zaw =

= 1 -

[

Aaa+

2xa xwAaw + Aww] – P

2/RoT[

Aaaa +

xwAaaw + 3xa

Aaww +

Awww ] (11)


Aaaa and Awww are the third virial

coefficient while Aaaw and Aaww are

the interaction third virial

coefficients. Hilesenrath [1 ]

tabulates values of B, C, and D

for dry air form 50 k to 1500 k.

Goff [2 ] give tables of Aaa’ Aww,

Awww and Aaw for air – water

mixtures for the temperature range

-900c.

Keyes [3] gives values from which

Aww and Awww can be deduced for pure

water vapoure. Mason and monchick

[4] have produced data from which

Aww may be evaluated, and they

stipulate that only the first,

second and third virial

coefficients have simple physical

interpretations. Goff and Gratch

[5] formulation sets

X3aAaaa=

xwAaaw= xa Aaww=0.0 (12)

and arrive at the generally

accepted equation [6]

Zaw = 1 -

[

Aaa+ 2xa xwAaw + Aww]

+P/Po( Awww )] (3)

Theory and reported experimental

deductions do not agree on the

interaction second virial

coefficient Aaw and considerable

uncertainties still exist [4] as

to the values of the interaction

third virial coefficients Aaaw and

Aaww Goff and Gratch [5] give

values of Z for dry air at

temperature varying from -1000C to

+60oCfor pressures ranging from

zero to 1100 mb. Their data for

moist air are reported at 25%

mixing ratio to degree of

saturation intervals from 0OC to

600C and at total pressures of

0,300, 700 and 1100 mb. They also

tabulate values corresponding to

pure water vapour (vapour over ice

and vapour over water) at

saturation or boiling point

temperatures of-l000C to +60

0C.

Hilsenratch [1] presents values

for steam at one and ten

atmospheres pressure for absolute

temperatures ranging from 3800K to

8500K. His data for dry air are

presented in a deviations form

leading of a table of (Zaa-1) x

105.

In all the literature

quoted above the accuracy level of

the data will be inadequate for

the theory developed later: a

theory that relies on small

differences. Practically, if the

compressibility factors of dry air

(Zaa) and air-water mixtures (Zaw)

are measured to the high degree of

accuracy demanded by the analysis,

then the precise values of the

interaction and virial

coefficients become an exercise in

statistical thermodynamics. That

the available measured data do not

satisfy this need of small

differences has led to the inverse

problem of evaluating Z from the

known second virial coefficients

and the theoretical predictions of

the interaction coefficients.

In this inverse problem,

statistical thermodynamics

considers water vapour molecules

as polar molecules with the force

constants (which determine the

second virial coefficients)

evaluated on the basis of the

Stockmayer 12-6-3 Potential

Function. Dry air, on the other

hand, is of non-polar molecules

with the force constants evaluated

from the Lenard Jones 12 - 6

Potential. Standard works in this

field are contained in books such

as by Tieu and Lienhard [7] and by

Hirschfelder et al [8]. Extensions

to moist air (as a binary mixture)

are reported by Hirschfelder et

al,[8] Shaddock [9] and Mason and

Monchick [4]. Statistical single -

value constants such as k, and exist for dry air (as of non-polar

molecules) and pure steam (as of

polar molecules). For dry air, the

reduced second virial coefficients

B*(=B/b ) and reduced temperatures

T* are available as one of the

Lenard-Jones . gases in a tabular

form [9, 10] for the range

0.30 ≤ T*= T(ε/k) ≤ 50.

Similar relations are presented by

Shaddock [9] quoting Rawlinson

[11] for a stockmayer Gas like


pure steam in the: range 0.80 ≤ T*

≤ 100.

An assumption made by Hirschfelder

et. al. is that the effective

interaction force constant between

a polar and a non-polar molecule

is identical in value to that

between two non-polar molecules.

With this assumption the

interaction coefficients of air-

water mixtures can be determined

for a good rage of temperatures.

In this work the second and third

virial coefficients for single-

component gases are taken from

existing results (Hilsenrath [11]

for air and Keyes [3] for steam).

The interaction second virial

coefficients are computed from

statistical data. The differences

between these theoretical values

and those due to Goff and Gratch

are compared. The effect on the

moist air compressibility factor

is found to be small. On the

partial pressure multiplier the

difference becomes practically

insignificant. This multiplier

(fss) is computed for air

saturated with water vapour at

total pressures varying from 800

mb to 110mb. The nearest relations

found in the literature, where f

is expressed explicitly in terms

of other variables, as in the

formula developed, are reported by

Harrison [12] using two data

sources: the first due to

Landsbaum, Dodd’s and Stutsman [3]

and the second using the data from

Webster [14]. Both are of the form

fss = [1 + (P-Pss)] C(T) (14)

(in our present notation)

where C(T) is a suitable function

of temperature but with the

dimensions of atmosphere.

2. THEORY

When moles of dry air alone

Occupies volume (V) at temperature

(T) under the pressure (pa) then

from a eqn.8

(V/ROT)= xa [1-

- (

)2

]

(15)

Similarly for xw moles of water

vapour alone, using eqn. 9 gives

(V/ROT)= xw [1-

–

]

(16)

If x + xw = 1.00 and the above

gases mix under Gibbs-dalton law,

then

+

V/ROT =xa +xw -

-

-

-

(17)

where xa =

and xw =

P1a and p

1w are idealized partial

pressures to yields the pressure

P.

Thus, on considering the gases as

Gibbs-Dalton gases one arrives at

the relation.

PV/ROT = 1-

[

Aaa+ Aww] -

[

Aaaa + Awww] (18)

Since +

= P.

However, for the real mixing

process, it is shown by eqn.l1

that the interaction coefficients

get involved. Thus if Pa and Pw are

the actual partial pressures on

mixing, then from eqn. 11

(Pa +Pw) V/ROT = 1-

[

Aaa+

2xaxwAaw + Aww] -

[

Aaaa +

3 xwAaaw + 3xa

Awww] +

…………….. (19)

Dividing eqn.19 with eqn.18 result

with series approximation in the

mixture partial pressures equation

(Pa + Pw)/P =1-

[2xaxwAaw]-

[3

xwAaaw + 3xa Aaww]+ (20)

It would be obvious from the above

that mixing of the dissimilar

gases leads to the inequality

pa + pw (21)

and that this inequality is due

to the interaction force constants


which consequently invalidate the

Gibbsalton Law.

When the third virial interaction

coefficients are neglected eqn.20

reduces to

pa + pw = P-

[2xaxwAaw] (21)

The above equation is quoted by

Goff [15] who also gives the

following relations between

partial pressures and mole

fractions:

Pa = xaP +

[-Aaa + xw(Aaa -2Aaw

+Aww)] P2 + (22)

It is easily verified that the

addition of the last two equations

results in eqn.21.

Since

xa + xw = 1.00 (24)

eqn.23 readily transforms to yield

Pw/P = xw-xa[ Aaa + 2xaxwAaw +

Aww]

(P/ROT) + Aaa (P/ROT) (25)

Pw/P=xw–xa(1-zaw)+ (1-zaa) (26)

Zaw=(PV/ROT)aw=1-

[

]P (27)

and

zaa = (PV/ROT)aa= 1- (

Aaa (28)

The last two equations follow from

eqn.10 but the longer

series/equation given in 13 can

also be used in eqn.26 for

numerical values of z.

A further reduction of eqn.26 when

xa 0.00 results in the final

expression

Pw/P=xw(2zaa – zaw)– (zaa - zaw) (29)

or

xw = [Pw/P+(zaa–zaw)]/(2zaa–zaw) (30)

The object of this analysis is the

evaluation of the mole fraction

(xw) when the vapour pressure (Pw)

is known. The problem therefore

demands that both zaa and zaw be

evaluated fairly accurately since

small differences are involved.

In order that mole fractions can

be determinate from partial

pressures we define the partial

pressure multiplier (faw) in the

form

xw =faw (Pw /P) (31)

Hence from eqn. 30, faw can be

written explicitly to give

faw=[1+(P/Pw)+(zaa–zaw)]/(2zaa–zaw)

(32)

The special case of wet – bulb

saturation or dew point

temperature would result in the

equivalent equations.

xss=[Pss/P+(zaa–zaw)]/(2zaa–zss) (33)

and

fss=[1+(P/Pss)(zaa–zss)]/(2zaa–zss)

(34)

Use of relations 30,32,33 or 34

will demand integrative techniques

since the Z terms cannot be

obtained unless the x terms are

found. Thus for a selected

saturation temperature and a given

barometric pressure, Pss is

obtained from tables, xss pss /p and use of this in equ, 13 result

in a rough estimate of Z since the

corresponding virial and

interaction coefficients are

determinate. Thereafter, use of

eqn.33 gives a better value of x

which is then inserted back in

eqn3 until both relations 13 and

33 are satisfied.

In this article, results are

presented only for the wet-bulb

saturation or dew point

temperatures due to space

limitations. However, the analysis

applies to other steam-air

mixtures since the vapour pressure

(Pw) isread1ly obtained.

3. DERIVATIONS

3.1 VIRIAL COEFFICIENTS FOR DRY

Air and Pure Water (Steam)

Table I gives the reported virial

coefficients for the single-


component gases: dry air and steam

from three sources. Agreements are

sufficiently close to permit no

further reference to theoretical

formulations. For substitution in

eqn.13, Hilsenrath's data are used

for air while those due to Keyes

are utilized for steam. It is

found that Hilsenrath's table

which is given in 10 K intervals

can be curve-fitted for the range

240 K <T <370 K with the equation

Aaa = 205.0067-.3653(T) +

0.003159(T2)–0.2674 x10

-5 (T

3) (35)

Use of the above relation reduces

inter potation errors.

3.2 The Interaction

Second Virial Coefficients

Theoretical results are obtained

in the manner suggested by

Shaddock which relies on the

intermolecular force constants for

dry air, pure water vapour and

air-vapour mixtures. These

statistical force constants are

reported as follows:

(i)Dry Air: (Lennard Jones 12-6

Potential): Non-polar molecules.

=3.522

(bo)aa=1.2615 =55.11x10

-3m3/kg-

mole

aa/k = 99.2 k

(ii)Pure Water Vapour (Stockmayer

12-6-3 Potential):

Polar molecules.

=2.65

(bo)ww=1.2615 =2.48x10

-3m3/kg-mole

ww/k = 380 k

(iii)Steam-Air Mixtures (Lennard

Jones 12-6 Potential):

Polar/non-polar molecules in a

binary mixture.

=3.053

(bo)aw=35.90x10-3m3/kg-mole

aw/k = 220.5 k

For the above force constants to

be valid in eqn.13, use of eqn.6

results in the equalities:

Aaa = -Baa = -(b0)aa

Aaw = -Baw = -(b0)aw

Aww = -Bww = -(b0)ww

where B* is the reduced second

virial interaction coefficient in

the volume series (eqn.2). Tables

exist to relate B* to the reduced

temperature (T*) for non-polar

substances (Bird and Spotz [10])

and for polar molecules

(Rowlinson[11]). Hence, for any

selected absolute temperature (T),

T.* can be evaluated and hence B*.

It follows that Aaa, Aww and Aaw are

determinate. The first two of

these parameters differ only

slightly from the data of Table 1.

The third, which is the

interaction second virial

coefficient, is tabulated in Table

2. These calculated theoretical

results differ significantly from

the experimental extrapolations

due to Goff [2].This difference is

of the order 50% above Goff’s data

for the temperature range covered.

However, when used in eqn. 13 the

effect on the compressibility

factor is not very significant.

This is illustrated in Fig. 1

where both zaa and zss are plotted

for saturation temperature of up

to 70 0C at a total pressure of

1100 mb.


Table 1: Virial Coefficients for Dry Air and Pure Water Substance from

Three Sources

t(0c) A aa X 103 (m3/ kg - mole)

A ww X 103

(m3/ kg - mole) Aww X 103 (m3/ kg mole Atmos )

Goff[2] Hilsenrath[1] Goff[2] Keyes[3] Goff[2] Keyes[3]

-30 21.6 21.360 - - - -

-10 15.7 15.755 2300 - - -

0 13.2 13.275 1830 1854.4 - 4130.4

10 10.9 10.988 1510 1519.5 - 2095.6

20 8.81 8.879 1260 1266.0 - 1131.9

30 6.87 6.932 1074 1070.5 - 641.3

40 5.09 5.130 924 916.8 - 379.0

50 3.44 3.457 803 794.1 - 233.2

60 1.91 1.897 705 694.9 110 146.5

70 0.49 0.435 625 613.3 72 96.7

80 -0.84 -0.946 558 545.7 48 65.44

90 -2.07 -2.261 501 489.0 33 45.26

100 - -33.528 - 441.0 - 32.01

Table 2: Interation Second Virial Coefficients for Moist air

t(0c) -30 10 0 10 20 30 40 50 60 70 80 90 100

Aaw x 10

3

(m3/kg

mole)

(a)Goff 51.8 45.0 42.0 39.3 36.8 34.5 32.3 30.4 28.5 26.8 25.2 23.7

(b)Theoretical 73.31 66.57 62.65 58.19 54.44 51.15 47.93 45.16 42.49 40.02 37..67 35.62 33.55

(b/a) 1.415 1.479 1.492 1.481 1.479 1.483 1.483 1.486 1.491 1.493 1.495 1.503


Fig.1 compressibility factors of dry air (Zaa) and saturated air (Zaa) at

1100mb total pressure


Fig 2. Compressibility factors for dry air (zaa) and for normal air at

saturation (Zss)


3.3 Compressibility Factors

Indications so far are that the

derived compressibility factors

will not differ significantly (in

the case of dry air alone) from

other reported data. This is

illustrated in Table 3 for dry air

at one atmosphere pressure. The

same trend was shown in Fig.1 for

1100 mb pressure. Table 4 gives

derived results for changing

barometric pressures while fig.2

gives a general trend within the

temperature and pressure limits of

normal air psychromery. When Table

4 is compared with Goff and

Gratch's tabulation [16] for Z ,it

would be observed that some minor

differences occur at the fourth

decimal point. These are due to

the idealized interaction

coefficients adapted in the

current analysis.

However, the vital significance of

the present study is that both Zaa

and Zss are calculated to an order

of magnitude that gives meaning to

their differences and thus permits

use of eqns.25-29.

3.4 The Partial Pressure

Multiplier (fSS)

The values of zaa (dry air) and zss

(vapour-saturated air) derived are

now utilized in eqns.33 and 34 to

obtain both the saturation mole-

fraction Xss and the multiplier fss

also at saturation. The results

are presented graphically in figs.

3 and 4.

In fig.3, a comparison is made

between the derived results at

1100 mb total pressure and the

tabulations of Webster [14],

Harrison [12] and Goff and Gratch

[5] at the same pressure.

Variation X is obtained using the

theoretical interaction force

constants with coefficients as

tabulated in Table 2(b). Curve Y

is a result of using Goff's

interaction coefficients (Table

2(a) in the establishment of Z.

Differences exhibited in these

drawings are not nearly as

significant as they look. Within

the range of normal air

psychometric (-100C to 60

oC) the

factor fss has reported values

between 1.0025 and 1.0065. The

effect on the specific humidity

(Table 5) can be shown to cause

differences of less than 0.570. In

particular, Goff and Gratch values

and the theoretical values lead to

specific humidity differences less

than 0.1070 at saturation.


Table 3: Comparison of Z values obtained from the present work to those

Tabulated by Hilsenrath[1] at one atmosphere pressure

Table 4. Derived Compressibility Factors of Water-Saturated Air and Dry

Air at Dew Point Temperature

P = 800 mb P - 840 mb

Tdp0c

Zss Zaa Zss Zaa

ss -10

0

10

20

30

40

50

60

0.999413

0.999505

0.999569

0.999590

0.999542

0.999373

0.998980

0.998180

0.999426

0.999535

0.999630

0.999711

0.999782

0.999844

0.999898

0.999945

0.999384

0.999482

0.999551

0.999551

0.999535

0.999376

0.999000

0.998228

0.999397

0.999512

0.999611

0.999696

0.999771

0.999836

0.999893

0.999942

P = 880 mb P = 920 mb

-10

0

10

20

30

40

5O

60

0.999356

0.999459

0.999533

0.999564

0.999528

0.999377

0.999017

0.99)8276

0.999368

0.999489

0.999593

0.999682

0.999.760

0.999828

0.999887

0.999939

0.999327

0.999435

0.999515

0.999550

0.999521

0.999382

0.999023

0.999320

0.999340

0.999465

0.999574

0.999668

0.999749

0.999820

0.999882

0.999937

,

T (k) Zaa

(Hilesenrath)

Zaa (present) t 0c

260 0.99923 0.999254

270 0.99937 0.999411 -10

280 0.99949 0.999531 0

290 0.99960 0.999634 10

300 0.99970 0.999724 20

310 0.99978 0.999802 30

320 0.99985 0.999870 40

330 0.99991 0.999930 50

340 0.99997 60s


Table 4 (contd.)

Tdp0c P = 960 mb P =1000 mb

10

0

10

20

30

40

50

60

zss zaa zss zaa

0.9992

0.999412

0.999496

0.999537

0.999513

0.999379

0.999047

0.999934

0.99311

0.999442

0.999556

0.999653

0.999738

0.999812

0.999877

0.999934

0.999270

0.999389

0.999478

0.999524

0.999505

0.999379

0.999059

0.999396

0.999283

0.999419

0.999537

0.999639

0.999728

0.999805

0.999872

0.999931

P = 1013. 25 mb P =1040 mb

-10

0

10

20

30

40

50

60

0.999260

0.999382

0.999472

0.999519

0.999502

0.999378

0.999063

0.998408

0.999254

0.999411

0.999531

0.999634

0.999724

0.999802

0.999870

0.999930

0.999241

0.999366

0.999460

0.999510

0.999498

0.999378

0.999070

0.999430

0.999254

0.999396

0.999519

0.999624

0.999717

0.999797

0.999867

0.999928


tdp P = 1100 mb

zaw zaa

-30

-10

0

10

20

30

40

50

60

70

80

90

100

0.998836

0.999196

0.999328

0.999429

0.999487

0.999482

0.999380

0.999090

0.998486

0.999346

0.995265

0.991639

0.985568

0.998838

0.999208

0.999357

0.999487

0.999599

0.999698

0.999783

0.999859

0.999925

0.999983

1.000035

1.000082

1.000125

Fig. 3: comparisons of the reported values of the functions fss with

theoretical derivations at 110mb total pressure


Fig. 4 .the factor fss as function of P and T

We note also that the data due to

Goff and Gratch cannot be

extrapolated without grave loss of

accuracy. It would be obvious that

as the vapour pressure approaches

the total pressure, fss would tend

to unity. This is represented by

eqn.26 when xa tends to zero. At a

saturation temperature

corresponding to the total

pressure, steam would exist as a

single-component mixture and

fss=1.0000. For the 1100 mb total

pressure, fg.3 gives the

corresponding temperature as 1020C

which is a graphical approximation

of 102.320C reported in the 1970

UK Steam Tables.

Table 5 also indicates that an

assumption of the _Gibbs-Dalton

Law (fss = 1.0000) under-estimates

the mole fraction and thus the

specific humidity at all

temperatures with the inherent

differences increasing with

temperature. The same trend is

obtained with decreasing total

pressures for a fixed temperature.

4. CONCLUDING REMARKS

This paper suggests a new

formulation for partial pressure

multipliers in air-water mixtures

of the atmosphere. This multiplier

is derived in a form that is

explicit in terms of such

measurable parameters, as partial

pressures and compressibility

factors of dry air and of moist

air. The simplicity lies in the

fact that virial and interaction

coefficients need not be known if

these compressibility factors can

be measured to a high degree of

accuracy. The theoretical approach

adapted for the second virial

interaction coefficients can be

seen as an idealized technique in

the absence of highly accurate

experimental data.

The final results do not differ

significantly from those derived

with the complicated formulations


of Goff and Gratch. These results

indicate that equally acceptable

values can follow from a simpler

analysis.

Table 5:Specific Humidity at Saturation Using Partial Pressure

Multipliers from 4 sources (1100 mb Total Pressure)

5. REFERENCES

1. Hiisenrath,J. et al, Tables of

Thermal Properties of Gases,

Washington,D.C

.,Superintendent of Documents,

U.S. Govt. Printing

Office.Natl.Bur.Std.Circ.,564,

74, 1955.

2. Goff,J.A., Standardization of

Thermodynamic Properties of

Moist Air, ASHVE Journal

Section, Heating, piping and

Air Conditioning,55,pp.118-

i28.I949.

3. Keyes, F.G., The Thermodynamic

Properties of Water Substance

00 to 150 C, J.Chem.Phys.,I5.p.

602,1947.

4. Mason,E.A. and Monchick,L .•

Survey of the Equation of

State and Transport Properties

of.Moist Gases; Humidity an?

Moisture,Vol.3,pp 257-

272,1965, Relnhold Pub.

Corp.,N.Y.

5. Goff,J.A.,and Gratch,S.,

Thermodynamic Properties of

Moist Air,Trans.Am.soc.

Heating Ventilating

Engineers,5I, p.125, 1945.

6. Jones, W.p., Air Conditioning

Engineering, Chap., pp.34-36.

Edward Arnold (Publishers),

Glasgow, Great Britain. 1973.

7. Tieu, C.L.,and Lienhard,J.H.,

statistical

Thermodynamics,H.R.W. Series

in Mechanical, Engineering,

Chap.,9,pp.241-

276,Holt,Rinehart and Winston

Inc.;N.Y., 1971.

8. Hirschfelder,J.o.;

Curtiss,C.F. and Bird,R.B.,

Molecular Theory of Gases and

t(oC)

Wss = (621.97) fssPss / (p – fss p

ss) g/kg air

-10 0 10 20

30 40 50 60

Webster's 1.482 3.492 7.048 13.55 25.03 44.84 78.79 138.0

Harrison 1.481 3.490 7.047 13.55 25.04 44.86 78.82 138.0

Goff

and

Gratch

1.479 3.489

7.049 13.57 25.08 44.96 79.04 138.6

Theoretical

(Present) 1.481 3.493 7.056 13.58 25.09 44.98 79.10

138.6

Ideal

Gases

(f =1.000)

1.472

3.472 7.016 13.50 24.94 44.70 78.55 137.5


Liquids,John Wiley and Sons.

Inc.,N.Y., 1964.

9. Chaadock.J.B, moist Air

Properties fromTabulated

Yirial Coefficients, Humidity

and· Moisture, Vo1.3, pp.273-2

kei84 Reinhold Pub. Corp.,

N.Y., 1965.

10. Bird,R.B. and Spotz,E.L.,The

Virial Equation of State.

University of Wisconsin NRL

Report CM599,I950.

11. Rowlinson.J.S., Transactions,

Faraday Society, 45. 1949

12. Harrison,L.p., Imperfect Gas

Relations,Humidity and

Moisture, Vol.3,pp.105-255,

Reinhold Pub. Corp.,

N.Y.,1965.

13. Landsbaum,E.M.;Dodds.W.s. and

Stutzman,L. Humidity of

Compressed Air, Ind.

Engr.Chem. ,47,p. 101,1955.

14. Webster,J.L .• The Effect of

Water Vapour Pressure of

Superimposed Air Pressure

jsoc. chem.ind.69.p 343, 1950

15. Goff,J.A. The Gibbs-Dalton Law Not aBasis for

Standardization. Humidity and

Moisture, ·op cit. pp. :285-

:287 .Reinhold Pub.Corp ,J.Y.

'1%5.

16. Goff,J.A. ,and Gratch,S•

SmithsonianMeteorological

Tables, edited by List, J.R ..

Washington, D.C., Smithsonian

Institution, Sixth Edition

First Reprint, p.333, 1958